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On the extension of positive definite kernels to topological algebras

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2020Embargo end date: 01 Jan 2020 United States English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 61 (issn: 0022-2488, eissn: 1089-7658,

Authors: Daniel Alpay; Ismael L. Paiva;

doi: 10.1063/5.0007301 , 10.48550/arxiv.2003.05632

arXiv: http://arxiv.org/abs/2003.05632

On the extension of positive definite kernels to topological algebras

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Abstract

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.

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United States

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Keywords

Mathematics - Functional Analysis, Algebra, FOS: Mathematics, Other Mathematics, Functional Analysis (math.FA)

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